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AP.STATS:

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CCSS.Math: , , , , an ecologist surveys the age of about a hundred trees in a local forest he uses a box-and-whisker plot to map his data shown below what is the range of tree ages that he surveyed what is the median age of a tree in the forest so first of all let's just let's make sure we understand what this box and whisker plot is even about this is really a way of seeing the spread of all of the different data points which is the age of the trees and to also give other information like what is the median and where does most of where the most of the ages of the tree sit so this whisker part so you can see this black part is a whisker this is the box and then this is another whisker right over here the whiskers tell us essentially the spread of all of the data so it says the lowest data point in the sample is an 8-year old tree I'm assuming that this this axis down here is in years and it says that the highest the oldest tree right over here is 50 years so if we want the range and when we think of range in a statistics point of view we're thinking of the highest data point - the lowest data point so it's going to be 50 minus 8 so we have a range of 42 so that's what the whiskers tell us it tells us that everything falls between 8 and 50 years including 8 years and 50 years now what the box does the box starts at well let me think explain it - this way the mid this line right over here this is the median this right over here is the median and so half of the ages are going to be less than this median we see right over here the median is 21 so this box and whiskers plot tells us that half of the ages of the trees are less than 21 and half are older than 21 and then these endpoints right over here these are the medians for each of those sections so this is the median for all the trees that are less than the real median or less than the main median so this is the middle of all of the ages of trees that are less than 21 this is the middle age for all of the trees that are greater than 21 or older than 21 and so these essentially are splitting we're actually splitting all of the data into four groups this we would call the first quartile so I'll call it q1 for a first quartile maybe do one q this is the first quartile roughly 1/4 of the trees because the way you calculate it sometimes a tree ends up in one point or another about 1/4 of the trees end up here 1/4 of the trees are between 14 and 21 a fourth are between 21 and it looks like 33 and then 1/4 are in this quartile so we call this the first quartile the second quartile the third quartile and the fourth quartile so to answer the question we already did the range there's a 42-year spread between the oldest and the youngest tree and then the median age of a tree in the forest is at 21 so even though you might have trees that are as old as 50 the median of the force is actually closer to the lower end of our entire our entire spectrum of all of the ages so the if you view median as your central tendency measurement it's only at 21 years and you can even see it it's closer to the left of the box and closer to the left the end of the left whisker then the end of the right whisker

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